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3 years ago

Which angle bisector was created by following the construction steps correctly? How do you know?

Mathematics

1 answer:

OverLord2011 [107]3 years ago

5 0

An angle bisector divides an angle into equal halves.

The bisection that follows the correct steps is Example 1

From the attached figure, we have:

Example 1

$\angle ABD = \angle DBC$

Example 2

$\angle ABD \ne \angle DBC$

When an angle is bisected, the resulting angles will be equal.

This means that the bisection in example 1 is correct, because angles ABD and DBC are congruent.

While the bisection in example 2 is incorrect, because angles ABD and DBC are not congruent.

Hence, the correct bisector is shown in Example 1.

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PLEASE HELP

sweet [91]

To model and solve our situation we are going to use the equation: $s= \frac{d}{t}$
where
$s$ is speed
$d$ is distance
$t$ is time

1. We know that the distance between the cities is 2400 miles, so $d=2400$ . We also know that the speed of the plane is 450 mi/h. Since we don't know the speed of the air, $S_{a}=?$ . We don't know how much the westward trip takes, so $t_{w}=?$ , and we also don't know how much the eastward trip takes, so $t_{e}=?$ .

Going westward. Here the plane is flying against the air, so we need to subtract the speed of the air from the speed of the plane:
$450-S_{a}= \frac{2400}{t_{w} }$
Going eastward. Here the plane is flying with the the air, so we need to add the speed of the air to the speed of the plane:
$450+S_{a}= \frac{2400}{t_{e} }$

2. We know for our problem that the round trip takes 11 hours; so the total time of the trip is 11, $t_{t}=11$ . Notice that we also know that the total time of the trip equals time of the tip going westward plus time of the trip going eastward, so $t_{t}=t_{w}+t_{e}$ . Since we know that the total trip takes 11 hours, we can replace that value in our total time equation and solve for $t_{w}$ :
$11=t_{w}+t_{e}$
$t_{w}=11-t_{e}$

Now we can replace $t_{w}$ in our going westward equation to model our round trip with a system of equations:
$450-S_{a}= \frac{2400}{t_{w}}$
$450-S_{a}= \frac{2400}{11-t_{e} }$ equation (1)
$450+S_{a}= \frac{2400}{t_{e}}$ equation (2)

3. To solve our system of equations, we are going to solve for $t_{e}$ in equations (1) (2):

From equation (1)
$450-S_{a}= \frac{2400}{11-t_{e} }$
$11-t_{e}= \frac{2400}{450-S_{a} }$
$-t_{e}= \frac{2400}{450-S_{a} } -11$
$t_{e}=11- \frac{2400}{450-S_{a} }$
$t_{e}= \frac{4950-11S_{a} -2400}{450-S_{a} }$
$t_{e}= \frac{2550-11S_{a} }{450-S_{a} }$ equation (3)

From equation (2):
$450+S_{a}= \frac{2400}{t_{e} }$
$t_{e}= \frac{2400}{450+S_{a} }$ equation (4)

Replacing (4) in (3)
$\frac{2400}{450+S_{a}} = \frac{2550-11S_{a}}{450-S_{a} }$
Now, we can solve for $S_{a}$ to find the speed of the wind:
$2400(450-S_{a})=(450+S_{a})(2550-11S_{a})$
$1080000-2400S_{a}=1147500-4950S_{a}+2550S_{a}-11(S_{a})^{2}$
$11(S_{a})^{2}-67500=0$
$11(S_{a})^{2}=67500$
$(S_{a})^{2}= \frac{67500}{11}$
$S_{a}=+/- \sqrt{ \frac{67500}{11} }$
Since speed cannot be negative, the solution of our equation is:
$S_{a}= \sqrt{ \frac{67500}{11} }$
$S_{a}=78.33$

We can conclude that the speed of the wind is 78 mph.

3 0

4 years ago

Substitution method x-7y=-9 -x+8y=10

max2010maxim [7]

Answer:

x = -2, y=1

Step-by-step explanation:

x-7y=-9---------------------equation 1

-x+8y=10-------------------equation 2

From equation 1, make x the subject of formula

x=7y-9----------------------equation 3

substituting x=7y-9 in equation 2,

-(7y-9)+8y=10

Expanding bracket

-7y+9+8y=10

Collecting like terms

8y-7y=10-9

y=1

substituting y=1 in 3

x=7(1)-9

x=7-9

x=-2

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3 years ago

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iren [92.7K]

3,6
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3 years ago

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likoan [24]

Answer:

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3 years ago

Use the ALEKS calculator to write 15/17 as a decimal rounded to the nearest tenth

mixas84 [53]

Answer:

15/17 is 0.88.

and rounded to the nearest tenth is 0.9

have a good day! c:

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3 years ago